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The Riemann solutions without vacuum states for compressible duct flows have been completely constructed in the paper [11]. However, the nonuniqueness of Riemann solutions due to a bifurcation of wave curves in state space is still an open problem. The purpose of this paper is to single out the physically relevant solution among all the possible Riemann solutions by comparing them with the numerical results of the axisymmetric Euler equations. Andrianov and Warnecke in [2] suggested using the entropy rate admissibility criterion to rule out the unphysical solutions. However, this criterion is not true for some test cases, i.e. the numerical result for axisymmetric three dimensional flows picks up an exact solution which does not satisfy the entropy rate admissibility criterion. Moreover, numerous numerical experiments show that the physically relevant solution is always located on a certain branch of the L-M curves. [ABSTRACT FROM AUTHOR]

Eshelby proved in 1957 that the strain field within a homogeneous ellipsoidal inclusion embedded in an infinite isotropic media is uniform, when the eigenstrain prescribed in the inclusion is uniform. This uniform strain field property was conjectured to hold exclusively for the ellipsoidally shaped inclusions. In recent studies the authors have discovered the arithmetic mean properties of the strains for N-fold (N is greater than 2 but unequal to 4) rotational symmetrical inclusions with uniform eigenstrains, called the arithmetic mean theorem of the Eshelby tensors. In this paper, we investigate the two-dimensional rotational symmetrical inclusions with rotational symmetrical eigenstrains. It is shown that for N-fold (N is greater than 4) rotational symmetrical inclusions with the same fold rotational symmetrical eigenstrains which are constant on the boundary of the inclusion, the arithmetic mean of the strains at N rotational symmetrical points presents special properties: For the points outside the inclusion, the arithmetic mean vanishes; for the points inside the inclusion, the arithmetic mean is in direct proportion to the eigenstrain on the boundary of the inclusion, with the coefficient tensor equal to the Eshelby tensor for circular inclusions. It is followed that the average strain over the inclusion domain and the line average of strains along a concentric circle inside the inclusion also equal the eigenstrains on the boundary of the inclusion multiplied by the Eshelby tensor for circular inclusions. These properties obtained in this paper can be safely reduced to the results for uniform eigenstrains shown in our former works. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the asymptotic and spectral analysis of a system of coupled Euler-Bernoulli and Timoshenko beams. The model is governed by a system of two coupled differential equations and a two parameter family of boundary conditions modelling the action of the self-straining actuators. The above equations of motion form a coupled linear hyperbolic system, which is equivalent to a single operator evolution equation in the energy space. That equation defines a semigroup of bounded operators. This is a dynamics generator of the semigroup which is our main object of interest in the present paper. We prove that for each set of boundary parameters, the dynamics generator has a compact inverse and this inverse operator belongs to class \documentclass{article}\pagestyle{empty}\usepackage{amsfonts}\begin{document}$\mathfrak{S}_p$\end{document} of compact operators with p > 1. We also show that if both boundary parameters are not purely imaginary numbers, then the dynamics generator is a nonselfadjoint operator in the energy space. However, its inverse operator is a finite-rank perturbation of a selfadjoint operator. The latter fact is crucial for the proof of the fact that the root vectors of the dynamics generator form a complete and minimal set in the energy space. We will use the spectral results in our forthcoming papers to prove that the dynamics generator of the system is a Riesz spectral operator in the sense of Dunford and to use the latter fact for the solution of several boundary and distributed controllability problems via the spectral decomposition method. [ABSTRACT FROM AUTHOR]

In this paper, the use of multirate-output controllers for sampled-data minimum H∞-norm regulation of civil engineering structures is investigated for the first time. The proposed control strategy contains a multirate sampling mechanism with different sampling period to each system measured-output. The civil engineering structures, studied in the paper, are considered to be assembled from finite elements obeying linear material laws, their displacements are small and the number of measured outputs is at least equal to the number of the disturbance forces and equal to the number of the control forces. The proposed technique relies on the equivalence between the action of multirate-output controllers and the action of static state feedback controllers, thus greatly simplifying the theoretical and computational aspects of the H∞-control problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical analysis of the autoconvolution equation x × x = y restricted to the interval [0,1]. We present a discrete constrained least squares approach and prove its convergence in Lp(0,1), 1≤ p ≤ ∞, where the regularization is based on a prescribed bound for the total variation of admissible solutions. This approach includes the case of non-smooth solutions possessing jumps. Moreover, an adaptation to the Sobolev space H1(0,1) is added. A numerical case study concerning the determination of non-monotone smooth and non-smooth functions x from the autoconvolution equation with noisy data y completes the paper. [ABSTRACT FROM AUTHOR]

The paper analyzes the motion of nonholonomic mechanical systems composed of two particles with imposition of various nonlinear limitations to the velocities of the particles - parallelism of velocities, equality of the intensities of velocities and perpendicularity of velocities. The analysis for such systems includes: equations of constraints, reactions of constraints, i.e. the mode of variations of such constraints, trajectories of the points of the systems, linear integrals for generalized velocities, i.e. cyclical coordinates. It is clearly demonstrated on these models that in the case of nonlinear nonholonomic constraints the Hamiltonian effect, in the general case, has no stationary value. Lastly, the equations of brachistochronic motion of described systems are derived and the brachitochrones of specified points are determined. [ABSTRACT FROM AUTHOR]

The article presents the papers published in the May 8, 2009 issue of "ZAMM" journal. It provides abstracts of several topics discussed in the paper. Topics include the effect of shear in fiber spinning, the onset of convection in a binary viscoelastic fluid saturated porous layer, and natural convection between two horizontal coaxial cylinders.

In this paper we use a layer potential analysis to show the existence of solutions for a Dirichlet-transmission problem for pseudodifferential Brinkman operators on Sobolev and Besov spaces associated to Lipschitz domains in compact boundaryless Riemannian manifolds. Compactness and invertibility properties of corresponding layer potential operators on Lp, Sobolev, or Besov scales are also obtained. [ABSTRACT FROM AUTHOR]

A transversely isotropic linear elastic half-space with depth wise axis of material symmetry containing a cylindrical cavity of finite length is considered to be under the effect of a time-harmonic torsion force applied on a ring at an arbitrary depth on the surface of the cylindrical cavity. With the aid of cosine transforms, the boundary value problem for the fundamental solution is reduced to a generalized Cauchy singular integral equation. The Cauchy integral equation involved in this paper is analytically investigated and the final equation is numerically solved with an in-depth attention. Integral representation of the stress and displacement are obtained, and is shown that their degenerated form to the static problem of isotropic material is coincide with existing solutions in the literature. To investigate the effect of material anisotropy, the results are numerically evaluated and illustrated. [ABSTRACT FROM AUTHOR]

In two recent papers necessary and sufficient conditions for a given system of second-order ordinary differential equations to be of Lagrangian form with additional dissipative forces were derived. We point out that these conditions are not independent and prove a stronger result accordingly. [ABSTRACT FROM AUTHOR]

In this paper we consider the von Kármán plate equations. We show that a suitable function, defined on the solution to these equations is subharmonic. Then we derive bounds on the integral of the second gradient of the solution. [ABSTRACT FROM AUTHOR]

In this paper the authors consider mechanical devices of rotational symmetry that can be seen as segments of an artificial worm or as a balloon for angioplasty. Continuing former work [7] the segment is now placed within a cylindrical or constricted rigid tube that will be touched or pressed during inflation of the segment. Both the segment's shape and the forces of contact are investigated. The main mathematical tool is the Principle of Minimal Potential Energy – handled as an optimal control problem with state constraint. The necessary optimality conditions are carefully analyzed and simulation results for characteristic examples are presented. The treatment of the problem is primarily mathematical but aiming at application. [ABSTRACT FROM AUTHOR]

In this paper we study the optimal control problem described by a hemivariational parabolic inclusion. We derive the existence of optimal solutions. Then we prove the convergence of optimal values for approximated control problems to the one for the original problem. Finally, we give a simple example. [ABSTRACT FROM AUTHOR]

The gasdynamic state of a plug of gas which was exhausted through a valve opened for a short time interval is quite inhomogeneous. In this paper a computational method based upon a onedimensional model is revived, and the complicated structure of the plug demonstrated in a realistic example. Der gasdynamische Zustand eines durch ein kurzzeitig geöffnetes Ventil entwichenen Gaspfropfens ist ganz uneinheitlich. Die vorgelegte Arbeit berechnet diesen Zustand auf der Basis des bekannten eindimensionalen Modells und zeigt ein realistisches Beispiel. [ABSTRACT FROM AUTHOR]

In this paper we consider an initial boundary value parabolic problem [cu + 𝒫[u]]_t - div(a ċ ν u) = f, with Preisach hysteresis 𝒫. The functions c, a, and the density function ψ of the Preisach operator are allowed to depend also on the space variable x. The equation is homogenized by considering a sequence of equations with spatially periodic data cε, aε, and ψε, where the spatial period ε converges to 0. Properties of hysteresis operators and the concept of two-scale convergence are used to show the convergence of the corresponding solutions to the solution of the homogenized problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss a parabolic system governed by bilinear control, modeled according to Newton's Law. At first we prove that the system is exactly null controllable in long time T > 0 by locally distributed bilinear control and we further prove the exact null controllability in long time T > 0 of the semilinear parabolic equation yt-Δ y + b |∇ y|2=ξοu with traditionally additive locally distributed control and the existence of the control optimal time for the system. Then, we deduce an exact controllability result to particular stationary functions when we are acting over the whole domain and to particular stationary functions vanishing outside some ball included in the control domain when the control domain is as small as we want. [ABSTRACT FROM AUTHOR]

Time scales have been introduced in order to unify the theories of differential and difference equations and in order to extend these cases to many other so-called dynamic equations. In this paper we consider a linear dynamic equation on a time scale together with a perturbed equation. We show that, if certain exponential dichotomy conditions are satisfied, then for any solution of the perturbed equation there exists a solution of the unperturbed equation that asymptotically differs from the solution of the perturbed equation no more than the order of the perturbation term. In order to show this perturbation theorem, we use many properties of the exponential function on time scales and derive several bounds for certain monomials that appear in the dynamic version of Taylor's formula. [ABSTRACT FROM AUTHOR]

In this paper we consider the oscillatory and asymptotic behavior of bounded solutions of second-order nonlinear perturbed dynamic equation (α(t)(xΔ(t))r)Δ+ F(t,xσ (t)) = G(t, xσ (t), xΔ (t)), t ∈𝕋 , (0.1) where r = k/l with k even and l odd positive integer. Some new sufficient conditions are obtained for all bounded solutions of (0.1) to be oscillatory. Several examples that dwell upon the importance of our results are also included. In particular, our criteria extend some earlier results. [ABSTRACT FROM AUTHOR]

In the present paper measured and simulated vibrations of viscoplastic plates under impulsive loading are compared to each other. The aim is to determine how accurately the measured deformations can be calculated by the chosen constitutive and structural theories. A first-order shear deformation shell theory assuming small strains and moderate rotations and viscoplastic laws are applied. In the experimental part of this study short time measurement techniques are applied to shock tubes in order to record fast loading processes and plate deformations. [ABSTRACT FROM AUTHOR]

This paper proves the existence of multiple solutions to the Coulomb friction problem with Signorini contact conditions in continuum linear elasticity. We consider a body lying on a rigid foundation and we propose a method in order to exhibit two solutions to the frictional contact problem when the friction coefficient is large enough: one solution which separates from the foundation and another one which remains stuck on the foundation. We apply the method to the simple class of problems with triangular bodies and linear displacement fields and we describe the cases in which such multiple solutions exist. Denoting by μ the friction coefficient, we come to the conclusion that such nonuniqueness cases may appear when μ>1. [ABSTRACT FROM AUTHOR]

This paper contributes to the novel approach of a deterministic risk analysis. We introduce a risk index, which is designed such that large values of the index indicate a deterministic risk. The approach is illustrated by two examples. The new risk index allows to give the “risk area” a quantitative meaning. [ABSTRACT FROM AUTHOR]

As indicated in the preface to this volume, it is essential in the engineering modelling process that the uncertainty of input parameters is captured and formulated in mathematical terms, so that it can be propagated through numerical computations. This is a necessary requirement for a proper assessment of the output variability. This introduction serves to discuss a number of mathematical approaches, focused around generalizations of probability theory, that are able to formalize the state of knowledge about parameter uncertainty. It is a very brief introduction to the realm of what is now commonly termed imprecise probabilities [2,4]. The papers collected in this volume all use one or more of these approaches; the purpose of this introduction is to point out some unifying ideas, remarks on interpretations (correspondence rules between model and reality, or semantics), and rudiments of a hierarchical classification. To keep the presentation simple, we shall consider a single input parameter called (upper case) A, while the specific values it may take (realizations) will be denoted by lower case letters. Further, the computational engineering model produces an output as a function F(A) of the input A. Uncertainty of multivariate models, correlations and stochastic field variables have their counterparts in all the approaches discussed below; for this we refer the reader to the literature cited at the end. [ABSTRACT FROM AUTHOR]

The generalized Lyapunov-Schmidt reduction is thoroughly investigated in this paper. Some new and known properties of the reduction are presented transparently. Among others we obtain two main results, an alternative proof of the equivalence of the generalized reduction and an approximation relation between the generalized Lyapunov-Schmidt reduction and the center manifold reduction. [ABSTRACT FROM AUTHOR]

This paper presents exact closed-formed solutions using elliptic integrals for large deflection analysis of elastics of a beam with variable are-length subjected to an inclined follower force. The beam is hinged at end but slides freely over the support at the other end. In the underformed state, the inclined follower force applied at any distance from the hinged end making an angle γ with respect to vertical axis while in the deformed state its direction remains at an angle γ from the normal to the beam axis. The set of nonlinear equations is obtained from the boundary conditions, and solved iteratively for the solutions. The effect of the direction and the opposition of the follower force on the beam bending behaviour is demonstrated. Comparisons of equilibrium configurations of the beam under non-follower force and follower force are also given. [ABSTRACT FROM AUTHOR]

In this paper, under the1-parameter closed homothetic motion in three dimensional Euclidean Space, we generalized the classical Holditch Theorem [1], for closed space curves by using their orthogonal projection on any fixed plane in space. We also obtained a formula equivalent to the result on the planar kinematics given by [6]. [ABSTRACT FROM AUTHOR]

In this paper a general integral formula for the fundamental solution of a linear partial difference equation with constant coefficients is investigated. For equations in two dimensional space. especially for the discretization of the Helmholtz, equation, special integral formulae are given and the convergence of corresponding integrals is proved. The limits of the fundamental solution at infinity are calculated in several cases. [ABSTRACT FROM AUTHOR]

The object of the paper is the derivative with respect to a second-order tensor. Basis-free as well as basis-related definitions of the derivative are addressed and compared. Special attention is focused on the derivative of a tensor function defined on a subset of all linear mappings within the real vector space, symmetric second-order tensors representing a most important example of such a subset. Due to a special definition of the simple contraction of fourth- and second-order tensors the well-known product rule of differentiation valid for scalar functions is proved to hold also for second-order tensor functions. Introducing a new tensor product of second-order tensors, another tensor differentiation rules as well as some useful tensor algebra operations are formulated. Applying this formalism the derivative of non-symmetric tensor power series is obtained in a closed form. This closed-formula solution is finally illustrated by some examples of continuum mechanics. As such, simple expressions for the derivative of the stretch and rotation tensor with respect to the deformation gradient and for the stresses conjugate to the logarithmic and more general Hill's strains are presented. [ABSTRACT FROM AUTHOR]

Steady laminar boundary layer flow and heat transfer of a micropolar fluid over a heated isothermal horizontal plate moving in a flowing stream has been studied in this paper. The cases corresponding to the isothermal horizontal plate moving in the same (parallel) or in the opposite (reverse) direction to the free stream are considered. Similarity and nonsimilarity equations of six special systems are reduced readily from universal formulation. The governing momentum, angular momentum, and energy equations have been solved numerically. The effects of buoyancy and relative velocity on the flow and temperature fields including surface friction and heat transfer rate are presented for a plate moving in parallel or reversely to the free stream. It is observed that micropolar fluids display drag reduction when compared to Newtonian fluids. [ABSTRACT FROM AUTHOR]

In this paper, we study five different types of problems in potential and viscous flows past intersecting circles or spheres in two and three dimensions, respectively, with different angles of intersection. We observe a striking resemblance in the form of the solutions in all these cases by introducing certain operators L and M which generate a group G. By introducing a procedure called ‘closure’ which determines the order of the group G, we give a general method to discuss the problem of flow past two intersecting circles or spheres in potential and Stokes flows with different angles of intersection. [ABSTRACT FROM AUTHOR]

In this paper, we wish to use complex potential methods to solve the fundamental complete plane strain (CPS) problems of a three-dimensional nonhomogeneous elastic body with a doubly-periodic set of cracks in the x1, x2 plane. We resolve the complete plane strain state, which is a special three-dimensional elastic system, into two linearly independent two-dimensional (plane) elastic systems by the superposition principle of force. Based on a suitable modification of Cauchy-type integrals, which is defined by the replacement of the Cauchy kernel 1/(t — z) by the Weierstrass zeta function ζ(t — z), the general representation for the solution is constructed, under some general restrictions the boundary value problem is reduced to a normal type singular integral equation with a Weierstrass zeta kernel, and the existence of an essentially unique solution is proved. [ABSTRACT FROM AUTHOR]

We consider meshless collocation methods for the numerical solution of transport processes described by hyperbolic conservation laws. The future goal is the construction of a robust and reliable meshfree discretization method for the equations of gas dynamics in complex geometries. In this paper we start with the simplest scalar model problems and analyze basic problems occurring in the grid-free approach. A topological condition on clouds of points is derived and several possible versions of a generalized Lax-Friedrichs scheme are discussed with respect to their numerical dissipation. A moving least-squares approach is followed to construct a positive discretization for solutions with shocks which is thoroughly analyzed and applied to test problems. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the mathematical strategies permitting the treatment of second order unilateral systems involving singular mass, damping, and stiffness matrices. Reduction methods are used here to transform second order differential inclusions in first order ones and classical results on differential inclusions are considered in order to obtain solutions. Friction and impact problems arising in Unilateral Mechanics are studied so as to illustrate the theoretical approach. [ABSTRACT FROM AUTHOR]

The paper contains a proposition of a model of adsorption in porous and granular materials. It is assumed that the mass source resulting from adsorption consists of two contributions: changes described by the Langmuir relation for bare sites and changes of the internal surface due to relaxation of porosity. The model is illustrated by a simple numerical example of a homogeneous adsorption process. [ABSTRACT FROM AUTHOR]

This paper shows that a third grade fluid (different from the model employed by Fosdick and Rajagopal, see Tigoiu [6]) has a unique solution when experiences a weakly perturbed flow and the rest state is asymptotically stable. This result is not in contradiction with the result obtained by Joseph, but it proves the limit in the application of the representation theorem of Coleman and Noll. [ABSTRACT FROM AUTHOR]

An equilibrium problem for a thermoelastic plate having a crack is considered. A mathematical model used to describe the process has the following unknown functions: a temperature θ, horizontal and vertical displacements $W=(w^1,\,w^2),\,w$, w of the mid-surface points, respectively. We use the so-called coupled thermoelastic model which, in particular, means a necessity of finding simultaneously the temperature and the displacements: $$\partial \theta /\partial t - \Delta \theta +\delta ^2(\partial /\partial t) ({\rm div}\,W-\Delta w)=f \, ,\eqno (1)$$ $$\Delta ^2w+\delta ^2\,\Delta \theta =0 \, ,\eqno (2)$$ $$-\sigma _{ij,\,j}+\delta ^2\theta _{,i}=0\,,\qquad i=1,\,2\,.\eqno (3)$$ Here δ is the positive parameter, f is the given function, $\theta _{,i}=\partial \theta /\partial x_i,\,\sigma _{ij}=\sigma _{ij}(W)$ are components of the integrated stress tensor, i, j = 1, 2, $$\sigma _{11}=\epsilon _{11}+\kappa \epsilon _{22},\;\sigma _{22}=\epsilon _{22}+\kappa \epsilon _{11},\;\sigma _{12}=(1-\kappa ) \epsilon _{12}\,,\eqno$$ $$\kappa ={\rm const}\,,\qquad 0<\kappa <\textstyle{1\over 2}\,.\eqno $$ By $\epsilon _{ij}=\epsilon _{ij}(W)$ we denote the strain tensor components of the mid-surface, $$\epsilon _{ij}(W)=\textstyle{1\over 2}(w^i_{,j}+w^j_{,i})\,,\qquad i,\,j=1,\,2\,.\eqno $$ The plate is assumed to have a crack. The presence of the crack entails the nonsmooth boundary of the domain in which the solution is found. The main peculiarity of the problem is related to the restriction of inequality type imposed on the solution $$[W] \nu \ge|[\partial w/\partial \nu ]|\,.\eqno (4)$$ Here [·] is the jump of a function on the crack faces, ν is the normal unit vector to the crack surface. This restriction has a physical nature and provides a mutual nonpenetration of the crack faces. Thus, we have to find the solution in a nonsmooth domain with boundary conditions of inequality type. In the paper a solvability of the problem is proved. The so-called cracks of minimal opening are considered. It is proved that the cracks of minimal opening provide an equilibrium state of the plate, which corresponds to the state without the crack. This means that such cracks do not introduce any singularity for the solution, and actually we can solve a boundary value problem without the crack. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a new class of generalized nonlinear implicit quasivariational inclusions for set-valued mappings. We construct some new iterative algorithms for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness. We prove the existence of solutions for this generalized nonlinear implicit quasivariational inclusions for set-valued mappings without compactness and the convergence of iterative sequences generated by the algorithms. We also give an application to generalized nonlinear implicit variational inequalities. [ABSTRACT FROM AUTHOR]

The asymptotics of the statistical estimators of stochastic programs has been derived out under the assumption that the samples are i.i.d. In some practical cases the samples may be not independent of each other. The limit distributions of the estimators in this case are studied in this paper. [ABSTRACT FROM AUTHOR]

In this short paper, practical estimates for the extreme eigenvalues of symmetric matrices and their inverses are obtained, and a criterion for Stieltjes matrices is presented. [ABSTRACT FROM AUTHOR]

Focuses on several developments in concerning the "Journal of Applied Mathematics and Mechanics," as of December 2004. Legal basis for the successful continuation of the journal; Acknowledgement of the contributions of doctor Walther Wessel to the journal; Importance of the review process for papers received for publication.